Related papers: Evolution equations of the probabilistic generaliz…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…
The evolution of probability distribution functions (PDFs) of continuous density, velocity and velocity derivatives ( deformation tensor) fields in the theory of cosmological gravitational instability are considered. We show that in the…
In this paper, we are interested in a generalised Vlasov equation, which describes the evolution of the probability density of a particle evolving according to a generalised Vlasov dynamic. The achievement of the paper is twofold. Firstly,…
A stationary distribution function that describes the entire processes of propagation of relativistic particles, including the transition between the ballistic and diffusion regimes, is obtained. The spacial component of the constructed…
The Voigt profile is one of the most used special function in optical spectroscopy. In particle physics a version of this profile which originates from relativistic Breit-Wigner resonance distribution often appears, however, in the…
.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…
The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre…
Weak gravitational lensing surveys have the potential to directly probe mass density fluctuation in the universe. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by…
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck…
We follow the evolution with sample thickness, of intensity statistics for localized light transmitted through layered media in a crossover from one to three dimensions occasioned by transverse disorder. The probability distribution of…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…
In the present review we survey the properties of a transcendental function of the Wright type, nowadays known as M-Wright function, entering as a probability density in a relevant class of self-similar stochastic processes that we…
Probabilistic diffusion models enjoy increasing popularity in the deep learning community. They generate convincing samples from a learned distribution of input images with a wide field of practical applications. Originally, these…
This paper is devoted to a statistical analysis of the fluctuations of velocity and acceleration produced by a random distribution of point vortices in two-dimensional turbulence. We show that the velocity probability density function…
The gravitational evolution of the cosmic one-point Probability Distribution Function (PDF) can be estimated using an analytic approximation that combines gravitational Perturbation Theory (PT) with the Edgeworth expansion around a Gaussian…
In this work, we propose a method to learn multivariate probability distributions using sample path data from stochastic differential equations. Specifically, we consider temporally evolving probability distributions (e.g., those produced…
Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the…
The probability distribution function (PDF) of the mass surface density of molecular clouds provides essential information about the structure of molecular cloud gas and condensed structures out of which stars may form. In general, the PDF…
We have measured the local and global statistics of singularity velocity, v, and have related these through the spatial correlation function of v. The distribution of v is a mixture of a mesoscopic distribution of global change in the…